To estimate the regression model in (REF ), we consider a dynamic generalization of the MAL distribution introduced in [1]} and [2]}, i.e. we consider the time-varying distribution \(\mbox{MAL}_p \left(\mu _t, D_t \tilde{\xi }, \, D_t \tilde{\Sigma } D_t \right)\) , with density function:
\(f_{Y_t} (y_t | \mu _t , D_t\tilde{\xi }, D_t\tilde{\Sigma } D_t, \mathcal {F}_{t-1}) = \frac{ 2\exp {\left\lbrace (y_t- \mu _t)^{\prime } D_t^{-1} \tilde{\Sigma }^{-1}\tilde{\xi } \right\rbrace }}{(2\pi )^{p/2} |D_t \tilde{\Sigma } D_t|^{1/2} } \left( \frac{\tilde{m}_t}{2+\tilde{d}}\right)^{\nu /2}K_{\nu }\left( \sqrt{(2+\tilde{d})\tilde{m}_t} \right).\nonumber \\[-0.1in]\) 
